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A034662 Sum of n-th powers of divisors of 20. 3

%I #31 Sep 08 2022 08:44:52

%S 6,42,546,9198,170898,3304182,65019786,1290094638,25700456418,

%T 513002215782,10250010815226,204900053024478,4097000260921938,

%U 81930001287820182,1638500006371967466,32769000031591352718,655370000156882923458

%N Sum of n-th powers of divisors of 20.

%H T. D. Noe, <a href="/A034662/b034662.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (42,-609,3948,-12180,16800,-8000).

%F a(n) = (1 + 2^n + 4^n)*(1 + 5^n). - _Bruno Berselli_, Apr 17 2014

%F G.f.: -6*(2800*x^5 -4060*x^4 +1974*x^3 -406*x^2 +35*x -1) / ((x -1)*(2*x -1)*(4*x -1)*(5*x -1)*(10*x -1)*(20*x -1)). - _Colin Barker_, Apr 20 2014

%t Total[#^Range[0, 20]&/@Divisors[20]] (* _Vincenzo Librandi_, Apr 17 2014 *)

%t Table[(1 + 2^n + 4^n) (1 + 5^n), {n, 0, 20}] (* _Bruno Berselli_, Apr 17 2014 *)

%o (Sage) [sigma(20,n) for n in range(0,16)] # _Zerinvary Lajos_, Jun 04 2009

%o (Magma) [DivisorSigma(n,20): n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)